Momentum and Collisions Preview Section 1 Momentum and

Momentum and Collisions Preview Section 1 Momentum and Impulse Section 2 Conservation of Momentum Section 3 Elastic and Inelastic Collisions © Houghton Mifflin Harcourt Publishing Company Section 1

Momentum and Collisions Section 1 What do you think? • Imagine an automobile collision in which an older model car from the 1960 s collides with a car at rest while traveling at 15 mph. Now imagine the same collision with a 2007 model car. In both cases, the car and passengers are stopped abruptly. • List the features in the newer car that are designed to protect the passenger and the features designed to minimize damage to the car. • How are these features similar? © Houghton Mifflin Harcourt Publishing Company

Momentum and Collisions Section 1 What do you think? • What are some common uses of the term momentum? • Write a sentence or two using the term momentum. • Do any of the examples provided reference the velocity of an object? • Do any of the examples reference the mass of an object? © Houghton Mifflin Harcourt Publishing Company

Momentum and Collisions Section 1 Momentum • Momentum (p) is proportional to both mass and velocity. • A vector quantity • SI Units: kg • m/s © Houghton Mifflin Harcourt Publishing Company

Momentum and Collisions Section 1 Momentum and Newton’s 2 nd Law • Prove that the two equations shown below are equivalent. F = ma and F = p/ t • Newton actually wrote his 2 nd Law as F = p/ t. – Force depends on how rapidly the momentum changes. © Houghton Mifflin Harcourt Publishing Company

Momentum and Collisions Section 1 Impulse and Momentum • The quantity F t is called impulse. – SI units: N • m or kg • m/s • Impulse equals change in momentum. – Another version of Newton’s 2 nd Law – Changes in momentum depend on both the force and the amount of time over which the force is applied. © Houghton Mifflin Harcourt Publishing Company

Momentum and Collisions Impulse-Momentum Theorem Click below to watch the Visual Concept © Houghton Mifflin Harcourt Publishing Company Section 1

Momentum and Collisions Changing momentum • Greater changes in momentum( p) require more force (F) or more time ( t). • A loaded truck requires more time to stop. – Greater p for truck with more mass – Same stopping force Section 1

Momentum and Collisions Section 1 Classroom Practice Problems • A 1350 kg car has a velocity of 22. 0 m/s to the north. When braking rapidly, it stops in 4. 50 s. – What was the momentum of the car before braking? – What is the magnitude of the force required to stop the car? • Answers: – 2. 97 x 104 kg • m/s to the north – 6. 60 x 103 N © Houghton Mifflin Harcourt Publishing Company

Momentum and Collisions Section 1 Stopping Time F t = p = mv • When stopping, p is the same for rapid or gradual stops. • Increasing the time ( t) decreases the force (F). – What examples demonstrate this relationship? • Air bags, padded dashboards, trampolines, etc • Decreasing the time ( t) increases the force (F). – What examples demonstrate this relationship? • Hammers and baseball bats are made of hard material to reduce the time of impact. © Houghton Mifflin Harcourt Publishing Company

Momentum and Collisions Section 1 Classroom Practice Problems • A 65 kg passenger in a car travels at a speed of 8. 0 m/s. If the passenger is stopped by an airbag in 0. 75 s, how much force is required? – Answer: 6. 9 x 102 N • If the car does not have an air bag and the passenger is instead stopped in 0. 026 s when he strikes the dashboard, by what factor does the force increase? – Answer: F = 2. 0 x 104 N so it is 29 times greater © Houghton Mifflin Harcourt Publishing Company

Momentum and Collisions Section 1 Now what do you think? • Imagine an automobile collision in which an older model car from the 1960 s collides with a car at rest while traveling at 15 mph. Now imagine the same collision with a 2007 model car. In both cases, the car and passengers are stopped abruptly. – List the features in the newer car that are designed to protect the passenger and the features designed to minimize damage to the car. – How are these features similar? © Houghton Mifflin Harcourt Publishing Company

Momentum and Collisions Section 1 Now what do you think? • How is momentum defined? • How is Newton’s 2 nd Law written using momentum? • What is impulse? • What is the relationship between impulse and momentum? © Houghton Mifflin Harcourt Publishing Company

Momentum and Collisions Section 2 What do you think? • Two skaters have equal mass and are at rest. They are pushing away from each other as shown. • Compare the forces on the two girls. • Compare their velocities after the push. • How would your answers change if the girl on the right had a greater mass than her friend? • How would your answers change if the girl on the right was moving toward her friend before they started pushing apart?

Momentum and Collisions Section 2 Momentum During Collisions • When the bumper cars collide, F 1 = -F 2 so F 1 t = -F 2 t, and therefore p 1 = - p 2. • The change in momentum for one object is equal and opposite to the change in momentum for the other object. • Total momentum is neither gained not lost during collisions.

Momentum and Collisions Section 2 Conservation of Momentum • Total momentum remains constant during collisions. • The momentum lost by one object equals the momentum gained by the other object. • Conservation of momentum simplifies problem solving.

Momentum and Collisions Conservation of Momentum Click below to watch the Visual Concept Section 2

Momentum and Collisions Section 2 Classroom Practice Problems • A 62. 0 kg astronaut on a spacewalk tosses a 0. 145 kg baseball at 26. 0 m/s out into space. With what speed does the astronaut recoil? – Step 1: Find the initial momentum of both astronaut and baseball. • Answer: zero because vi = 0 for both – Step 2: Since pi = 0, then pf, astronaut= -pf, baseball – Step 3: Substitute and solve for vf, astronaut • Answer: -0. 0608 m/s or -6. 08 cm/s • Does a pitcher recoil backward like the astronaut when throwing the ball? Explain.

Momentum and Collisions Section 2 Classroom Practice Problem • Gerard is a quarterback and Tyler is a defensive lineman. Gerard’s mass is 75. 0 kg and he is at rest. Tyler has a mass of 112 kg, and he is moving at 8. 25 m/s when he tackles Gerard by holding on while they fly through the air. With what speed will the two players move together after the collision? • Answer: 4. 94 m/s

Momentum and Collisions Section 2 Now what do you think? • Two skaters have equal mass and are at rest. They are pushing away from each other as shown. • Compare the forces on the two girls. • Compare their velocities after the push. • How would your answers change if the girl on the right had a greater mass than her friend? • How would your answers change if the girl on the right was moving toward her friend before they started pushing apart?

Momentum and Collisions Section 3 What do you think? • Collisions are sometimes described as elastic or inelastic. To the right is a list of colliding objects. Rank them from most elastic to most inelastic. • What factors did you consider when ranking these collisions? 1. 2. 3. 4. 5. A baseball and a bat A baseball and a glove Two football players Two billiard balls Two balls of modeling clay 6. Two hard rubber toy balls 7. An automobile collision

Momentum and Collisions Perfectly Inelastic Collisions • Two objects collide and stick together. – Two football players – A meteorite striking the earth • Momentum is conserved. • Masses combine. Section 3

Momentum and Collisions Section 3 Classroom Practice Problems • An 2. 0 x 105 kg train car moving east at 21 m/s collides with a 4. 0 x 105 kg fully-loaded train car initially at rest. The two cars stick together. Find the velocity of the two cars after the collision. – Answer: 7. 0 m/s to the east • Now calculate the kinetic energy of the two cars before and after the collision. Was kinetic energy conserved? – Answer: KEbefore= 4. 4 x 107 J, KEafter= 1. 5 x 107 J • KE is not conserved. It is less after the collision.

Momentum and Collisions Inelastic Collisions • Kinetic energy is less after the collision. – It is converted into other forms of energy. • Internal energy - the temperature is increased. • Sound energy - the air is forced to vibrate. • Some kinetic energy may remain after the collision, or it may all be lost. Section 3

Momentum and Collisions Section 3 Elastic Collisions • Objects collide and return to their original shape. • Kinetic energy remains the same after the collision. • Perfectly elastic collisions satisfy both conservation laws shown below.

Momentum and Collisions Section 3 Elastic Collisions • Two billiard balls collide head on, as shown. Which of the following possible final velocities satisfies the law of conservation of momentum? – vf, A = 2. 0 m/s, vf, B = 2. 0 m/s – vf, A = 0 m/s, vf, B = 4. 0 m/s – vf, A = 1. 5 m/s, vf, B = 2. 5 m/s • Answer: all three m = 0. 35 kg v = 4. 0 m/s v = 0 m/s

Momentum and Collisions Section 3 Elastic Collisions • Two billiard balls collide head on, as shown. Which of the following possible final velocities satisfies the law of conservation of kinetic energy? – vf, A = 2. 0 m/s, vf, B = 2. 0 m/s – vf, A = 0 m/s, vf, B = 4. 0 m/s – vf, A = 1. 5 m/s, vf, B = 2. 5 m/s • Answer: only vf, A = 0 m/s, vf, B = 4. 0 m/s m = 0. 35 kg v = 4. 0 m/s v = 0 m/s

Momentum and Collisions Types of Collisions Click below to watch the Visual Concept Section 3

Momentum and Collisions Types of Collisions Section 3

Momentum and Collisions Section 3 Now what do you think? • To the right is a list of colliding objects. Rank them from most elastic to most inelastic. • What factors did you consider when ranking these collisions? 1. 2. 3. 4. 5. A baseball and a bat A baseball and a glove Two football players Two billiard balls Two balls of modeling clay 6. Two hard rubber toy balls 7. An automobile collision